I think Maggie and Billie are ok by themselves, and to some extent Rosie (but seriously, why call her Rosie and not Rose??). Evie does sound really cutesy by itself. My sister's name is Evie, but her full name is Genevieve. Milly is another super cute name, I think it would just be weird by itself. I know at least three Millys/Millies, but their full names are all Amelia.

Another name is Edie. I really like Edie, and I reckon it would work pretty well just by itself. Also Tess, Kirsty, Lucy, Georgie, Sadie, maybe Abby, Molly and Libby. Definitely not Ellie, Allie, Tilly, Izzie, Maisie, Katie, Pippa, Lexie, Trixie...

Romy would probably be ok. It's better than Rosemary. It's much less cute-sounding than lots of others.